Approximation of Poisson integrals by de la Valleé-Poussin sums in uniform and integral metrics

Abstract

On the classes of Poisson integrals of functions belonging to the unit balls of the spaces $L_s , 1 ≤ s ≤ ∞$, we establish asymptotic equalities for upper bounds of approximations by de la Vallée-Poussin sums in the uniform metric. Asymptotic equalities are also obtained for the case of approximation by de la Vallée-Poussin sums in the metrics of the spaces $L_s , 1 ≤ s ≤ ∞$, on the classes of Poisson integrals of functions belonging to the unit ball of the space $L_1$.